论文标题
分类跟踪的本地术语
Local terms for the categorical trace
论文作者
论文摘要
在本文中，我们介绍了Artin堆栈的分类“真实术语”地图，并表明它们具有适当的推动力，平稳的回调和专业化的上下班。特别是，我们将[VA2]的结果推广到此设置。 作为应用程序，我们提供了[AGKRRV]中两个定理的证据。也就是说，我们表明，Frobenius内态性的“真实本地术语”与“天真的本地术语”相吻合，并与！ - pushforwards通勤。后一个结果是经典的Grothendieck-Lefschetz Trace公式的绝对版本。
In this paper we introduce the categorical "true local terms" maps for Artin stacks and show that they are additive and commute with proper pushforwards, smooth pullbacks and specializations. In particular, we generalizing results of [Va2] to this setting. As an application, we supply proofs of two theorems stated in [AGKRRV]. Namely, we show that the "true local terms" of the Frobenius endomorphism coincide with the "naive local terms" and that the "naive local terms" commute with !-pushforwards. The latter result is a categorical version of the classical Grothendieck--Lefschetz trace formula.
